[{"key":"dc.contributor.author","value":"Takeru Matsuda","language":null},{"key":"dc.coverage.spatial","value":"Banff (Alta.)","language":null},{"key":"dc.date.accessioned","value":"2019-10-09T05:00:43Z","language":null},{"key":"dc.date.available","value":"2019-10-09T08:24:02Z","language":null},{"key":"dc.date.issued","value":"2019-04-11T09:40","language":null},{"key":"dc.identifier.other","value":"BIRS-VIDEO-201904110940-Matsuda","language":null},{"key":"dc.identifier.other","value":"BIRS-VIDEO-19w5188-32194","language":null},{"key":"dc.identifier.uri","value":"http:\/\/hdl.handle.net\/2429\/71866","language":null},{"key":"dc.description.abstract","value":"I talk about two recent studies on singular value shrinkage.\n1. We develop singular value shrinkage priors for the mean matrix parameters in the matrix-variate normal model with known covariance matrices. Our priors are superharmonic and put more weight on matrices with smaller singular values. They are a natural generalization of the Stein prior. Bayes estimators and Bayesian predictive densities based on our priors are minimax and dominate those based on the uniform prior in finite samples. In particular, our priors work well when the true value of the parameter has low rank.\n2. We develop an empirical Bayes (EB) algorithm for the matrix completion problems. The EB algorithm is motivated from the singular value shrinkage estimator for matrix means by Efron and Morris. Numerical results demonstrate that the EB algorithm attains at least comparable accuracy to existing algorithms for matrices not close to square and that it works particularly well when the rank is relatively large or the proportion of observed entries is small. \nApplication to real data also shows the practical utility of the EB algorithm.","language":null},{"key":"dc.format.extent","value":"30.0 minutes","language":null},{"key":"dc.format.mimetype","value":"video\/mp4","language":null},{"key":"dc.language.iso","value":"eng","language":null},{"key":"dc.publisher","value":"Banff International Research Station for Mathematical Innovation and Discovery","language":null},{"key":"dc.relation","value":"19w5188: New and Evolving Roles of Shrinkage in Large-Scale Prediction and Inference","language":null},{"key":"dc.relation.ispartofseries","value":"BIRS Workshop Lecture Videos (Banff, Alta)","language":null},{"key":"dc.rights","value":"Attribution-NonCommercial-NoDerivatives 4.0 International","language":null},{"key":"dc.rights.uri","value":"http:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0\/","language":null},{"key":"dc.subject","value":"Mathematics","language":null},{"key":"dc.subject","value":"Statistics","language":null},{"key":"dc.title","value":"Singular value shrinkage priors and empirical Bayes matrix completion","language":null},{"key":"dc.type","value":"Moving Image","language":null},{"key":"dc.description.affiliation","value":"Non UBC","language":null},{"key":"dc.description.reviewstatus","value":"Unreviewed","language":null},{"key":"dc.description.notes","value":"Author affiliation: University of Tokyo","language":null},{"key":"dc.description.scholarlevel","value":"Researcher","language":null},{"key":"dc.date.updated","value":"2019-10-09T05:00:43Z","language":null}]